On uniqueness and existence of viscosity solutions of fully nonlinear second‐order elliptic PDE's

1989/01/01 by Hitoshi Ishii · 6 citations
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · doi:10.1002/cpa.3160420103

openalex publication_date 1989/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/22

Abstract

Abstract We prove several comparison and existence theorems for viscosity solutions of fully nonlinear degenerate elliptic equations. One of them extends some recent uniqueness results by Jensen. Some establish the uniqueness of solutions for second‐order Isaacs' equations and hence include the uniqueness results for Bellman equations by P.‐L. Lions. Our comparison results apply even for discontinuous solutions and so Perron's method readily yields the existence of continuous solutions.

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• Hitoshi Ishii [wikipedia]